1,375 research outputs found

    Checkerboard Julia Sets for Rational Maps

    Full text link
    In this paper, we consider the family of rational maps \F(z) = z^n + \frac{\la}{z^d}, where n2n \geq 2, d1d\geq 1, and\la \in \bbC. We consider the case where \la lies in the main cardioid of one of the n1n-1 principal Mandelbrot sets in these families. We show that the Julia sets of these maps are always homeomorphic. However, two such maps \F and FμF_\mu are conjugate on these Julia sets only if the parameters at the centers of the given cardioids satisfy \mu = \nu^{j(d+1)}\la or \mu = \nu^{j(d+1)}\bar{\la} where j \in \bbZ and ν\nu is an n1stn-1^{\rm st} root of unity. We define a dynamical invariant, which we call the minimal rotation number. It determines which of these maps are are conjugate on their Julia sets, and we obtain an exact count of the number of distinct conjugacy classes of maps drawn from these main cardioids.Comment: 25 pages, 14 figures; Changes since March 19 version: added nine figures, fixed one proof, added a section on a group actio

    Bifurcations in the Space of Exponential Maps

    Full text link
    This article investigates the parameter space of the exponential family zexp(z)+κz\mapsto \exp(z)+\kappa. We prove that the boundary (in \C) of every hyperbolic component is a Jordan arc, as conjectured by Eremenko and Lyubich as well as Baker and Rippon. In fact, we prove the stronger statement that the exponential bifurcation locus is connected in \C, which is an analog of Douady and Hubbard's celebrated theorem that the Mandelbrot set is connected. We show furthermore that \infty is not accessible through any nonhyperbolic ("queer") stable component. The main part of the argument consists of demonstrating a general "Squeezing Lemma", which controls the structure of parameter space near infinity. We also prove a second conjecture of Eremenko and Lyubich concerning bifurcation trees of hyperbolic components.Comment: 29 pages, 3 figures. The main change in the new version is the introduction of Theorem 1.1 on the connectivity of the bifurcation locus, which follows from the results of the original version but was not explicitly stated. Also, some small revisions have been made and references update

    Stability of Intercelular Exchange of Biochemical Substances Affected by Variability of Environmental Parameters

    Full text link
    Communication between cells is realized by exchange of biochemical substances. Due to internal organization of living systems and variability of external parameters, the exchange is heavily influenced by perturbations of various parameters at almost all stages of the process. Since communication is one of essential processes for functioning of living systems it is of interest to investigate conditions for its stability. Using previously developed simplified model of bacterial communication in a form of coupled difference logistic equations we investigate stability of exchange of signaling molecules under variability of internal and external parameters.Comment: 11 pages, 3 figure

    Reversible skew laurent polynomial rings and deformations of poisson automorphisms

    Get PDF
    A skew Laurent polynomial ring S = R[x(+/- 1); alpha] is reversible if it has a reversing automorphism, that is, an automorphism theta of period 2 that transposes x and x(-1) and restricts to an automorphism gamma of R with gamma = gamma(-1). We study invariants for reversing automorphisms and apply our methods to determine the rings of invariants of reversing automorphisms of the two most familiar examples of simple skew Laurent polynomial rings, namely a localization of the enveloping algebra of the two-dimensional non-abelian solvable Lie algebra and the coordinate ring of the quantum torus, both of which are deformations of Poisson algebras over the base field F. Their reversing automorphisms are deformations of Poisson automorphisms of those Poisson algebras. In each case, the ring of invariants of the Poisson automorphism is the coordinate ring B of a surface in F-3 and the ring of invariants S-theta of the reversing automorphism is a deformation of B and is a factor of a deformation of F[x(1), x(2), x(3)] for a Poisson bracket determined by the appropriate surface

    The effect of precipitation and application rate on dicyandiamide persistence and efficiency in two Irish grassland soils

    Get PDF
    peer-reviewedThe nitrification inhibitor dicyandiamide (DCD) has had variable success in reducing nitrate (NO3-) leaching and nitrous oxide (N2O) emissions from soils receiving nitrogen (N) fertilisers. Factors such as soil type, temperature and moisture have been linked to the variable efficacy of DCD. Since DCD is water soluble it can be leached from the rooting zone where it is intended to inhibit nitrification. Intact soil columns (15 cm diameter by 35 cm long) were taken from luvic gleysol and haplic cambisol grassland sites and placed in growth chambers. DCD was applied at 15 or 30 kg DCD ha-1, with high or low precipitation. Leaching of DCD, mineral N and the residual soil DCD concentrations were determined over eight weeks High precipitation increased DCD in leachate and decreased recovery in soil. A soil x DCD rate interaction was detected for the DCD unaccounted (proxy for degraded DCD). In the cambisol degradation of DCD was high (circa 81%) and unaffected by DCD rate. In contrast DCD degradation in the gleysol was lower and differentially affected by rate, 67 and 46% for the 15 and 30 kg ha-1 treatments, respectively. Differences DCD degradation rates between soils may be related to differences in organic matter content and associated microbiological activity. Variable degradation rates of DCD in soil, unrelated to temperature or moisture, may contribute to varying DCD efficacy. Soil properties should be considered when tailoring DCD strategies for improving nitrogen use efficiency and crop yields, through the reduction of reactive nitrogen loss.This research was financially supported under the National Development Plan, through the Research Stimulus Fund, administered by the Department of Agriculture, Food and the Marine under grants 07519 and 07545

    Truncated states obtained by iteration

    Full text link
    Quantum states of the electromagnetic field are of considerable importance, finding potential application in various areas of physics, as diverse as solid state physics, quantum communication and cosmology. In this paper we introduce the concept of truncated states obtained via iterative processes (TSI) and study its statistical features, making an analogy with dynamical systems theory (DST). As a specific example, we have studied TSI for the doubling and the logistic functions, which are standard functions in studying chaos. TSI for both the doubling and logistic functions exhibit certain similar patterns when their statistical features are compared from the point of view of DST. A general method to engineer TSI in the running-wave domain is employed, which includes the errors due to the nonidealities of detectors and photocounts.Comment: 10 pages, 22 figure

    Computing periodic orbits using the anti-integrable limit

    Full text link
    Chaotic dynamics can be effectively studied by continuation from an anti-integrable limit. Using the Henon map as an example, we obtain a simple analytical bound on the domain of existence of the horseshoe that is equivalent to the well-known bound of Devaney and Nitecki. We also reformulate the popular method for finding periodic orbits introduced by Biham and Wenzel. Near an anti-integrable limit, we show that this method is guaranteed to converge. This formulation puts the choice of symbolic dynamics, required for the algorithm, on a firm foundation.Comment: 11 Pages Latex2e + 1 Figure (eps). Accepted for publication in Physics Lettes

    Increased expression of a microRNA correlates with anthelmintic resistance in parasitic nematodes

    Get PDF
    Resistance to anthelmintic drugs is a major problem in the global fight against parasitic nematodes infecting humans and animals. While previous studies have identified mutations in drug target genes in resistant parasites, changes in the expression levels of both targets and transporters have also been reported. The mechanisms underlying these changes in gene expression are unresolved. Here, we take a novel approach to this problem by investigating the role of small regulatory RNAs in drug resistant strains of the important parasite Haemonchus contortus. microRNAs (miRNAs) are small (22 nt) non-coding RNAs that regulate gene expression by binding predominantly to the 3′ UTR of mRNAs. Changes in miRNA expression have been implicated in drug resistance in a variety of tumor cells. In this study, we focused on two geographically distinct ivermectin resistant strains of H. contortus and two lines generated by multiple rounds of backcrossing between susceptible and resistant parents, with ivermectin selection. All four resistant strains showed significantly increased expression of a single miRNA, hco-miR-9551, compared to the susceptible strain. This same miRNA is also upregulated in a multi-drug-resistant strain of the related nematode Teladorsagia circumcincta. hco-miR-9551 is enriched in female worms, is likely to be located on the X chromosome and is restricted to clade V parasitic nematodes. Genes containing predicted binding sites for hco-miR-9551 were identified computationally and refined based on differential expression in a transcriptomic dataset prepared from the same drug resistant and susceptible strains. This analysis identified three putative target mRNAs, one of which, a CHAC domain containing protein, is located in a region of the H. contortus genome introgressed from the resistant parent. hco-miR-9551 was shown to interact with the 3′ UTR of this gene by dual luciferase assay. This study is the first to suggest a role for miRNAs and the genes they regulate in drug resistant parasitic nematodes. miR-9551 also has potential as a biomarker of resistance in different nematode species
    corecore